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SUMMARY:An h-principle for algebraic bundles and applications  - Alexis Au
 monier (Cambridge)
DTSTART:20231018T150000Z
DTEND:20231018T160000Z
UID:TALK207082@talks.cam.ac.uk
CONTACT:Oscar Randal-Williams
DESCRIPTION: A homotopy principle (h-principle for short) often takes the 
 form of a theorem approximating the topology of a space of solutions of a 
 differential equation via homotopical methods. In this talk\, I will descr
 ibe an h-principle for sections of algebraic vector bundles on projective 
 complex varieties subject to differential relations. Combined with some al
 gebraic topology\, I will show how it can be used to compute parts of the 
 cohomology of various spaces from classical algebraic geometry. Examples i
 nclude: the locus of smooth hypersurfaces in a very ample linear system\, 
 spaces of smooth complete intersections\, and spaces of holomorphic maps t
 o projective spaces.
LOCATION:MR13
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